Complex Numbers with TI-Nspire™ CAS

Complex Numbers

with

TI-Nspire? CAS

Forest W. Arnold

September 2020

Typeset in LATEX.

Copyright ? 2020 Forest W. Arnold

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Trademarks

TI-Nspire is a registered trademark of Texas Instruments, Inc.

Attribution

Most of the examples in this article are from A First Course in Linear Algebra

an Open Text by Lyrix Learning, base textbook version 2017 - revision A, by K.

Kuttler.

The text is licensed under the Creative Commons License (CC BY) and is available for download at the link

.

1

Introduction

This article describes and demonstrates how to use TI-Nspire¡¯s builtin functions

to

? add and subtract complex numbers,

? multiply and divide complex numbers,

? graph complex numbers in a complex plane,

? use the Polar Form of complex numbers,

? convert complex numbers from rectangular to polar form and vice versa,

? use De Moivre¡¯s Theorem to find powers and roots of complex numbers.

Some of the TI-Nspire examples in this article require the CAS version of TINspire.

2

2.1

Complex Numbers

Definitions

Complex numbers extend the real numbers, adding functionality to solve problems such as x2 + 4 = 0. Problems like this can not be solved with real numbers¡Ì

since the solution involves taking the square root of a negative number; e.g.,

x = ?4.

The set of real numbers is a subset of the set of complex numbers. The set of

complex numbers includes an imaginary number, i such that i2 = ?1. Complex

numbers are represented in standard form as z = a + bi, where a is the real part

and b is the imaginary part of the complex number z. With this form, a real number is simply a + 0i and a pure imaginary number is 0 + bi. Standard form of a

complex number is also called rectangular form.

2.2

Complex Numbers with TI-Nspire

Enabling Complex Numbers

1

To enable complex numbers in TI-Nspire, open the Document Settings dialog

by selecting the File - Settings - Document Settings... menu item, then choose

either Rectangular or Polar from the Real or Complex Format drop-down list:

Note: The polar form for complex numbers is discussed in a subsequent section of this article.

Entering Complex Numbers

The imaginary number i is inserted in a TI-Nspire application by either typing

@i or selecting its symbol from the Symbols pane in the Documents Toolbox. A

complex number in standard form is inserted by typing the number as a+b@i. An

example of entering a complex number in a calculator page is

After the enter key is pressed, @i is replaced with the symbol for the imaginary

number:

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